‎Enhancing Big Data Governance Framework Implementation Using Novel Fuzzy Frank Operators‎: ‎An Application to MADM Process

الموضوعات : Transactions on Fuzzy Sets and Systems

Hamza Iftikhar ¹ (Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan. )
Faisal  Mehmood ² (School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning 530006, China.)

تاريخ الإرسال : 24 الإثنين , ربيع الأول, 1445 تاريخ التأكيد : 08 الإثنين , رمضان, 1445 تاريخ الإصدار : 28 الثلاثاء , شوال, 1445

الکلمات المفتاحية: Picture fuzzy set‎, ‎Complex picture fuzzy set‎, ‎Frank operations‎, ‎Averaging operators‎, ‎Geometric operators‎.,

ملخص المقالة :

In today's data-driven landscape‎, ‎to ensure continuous survival and betterment‎, ‎the implementation of a robust Big Data Governance Framework (BDGF) is imperative for organizations to effectively manage and harness the potential of their vast data resources‎. ‎The BDGF serves no purpose when implemented in a random manner‎. ‎This article delves into the complex decision-making challenges that emerge in the context of implementation of the BDGF under uncertain conditions‎. ‎Specifically‎, ‎we aim to analyze and evaluate the BDGF performance using the Multi-Attribute Decision-Making (MADM) techniques aiming to address the intricacies of big data governance uncertainties‎. ‎To achieve our objectives‎, ‎we explore the application of Frank operators within the framework of complex picture fuzzy (CPF) sets (CPFs)‎. ‎We introduce complex picture fuzzy Frank weighted averaging (CPFFWA) and complex picture fuzzy Frank ordered weighted averaging (CPFFOWA) operators to enable more accurate implementation of the BDGF‎. ‎Additionally‎, ‎we rigorously examine the reliability of these newly proposed fuzzy Frank (FF) operators (FFAOs)‎, ‎taking into consideration essential properties such as idempotency‎, ‎monotonicity‎, ‎and boundedness‎. ‎To illustrate the practical applicability of our approach‎, ‎we present a case study that highlights the decision-making challenges encountered in the implementation of the BDGF‎. ‎Subsequently‎, ‎we conduct a comprehensive numerical example to assess various BDGF implementation options using the MADM technique based on complex picture fuzzy Frank aggregation (CPFFA) operators‎. ‎Furthermore‎, ‎we perform a comprehensive comparative assessment of our proposed methodology‎, ‎emphasizing the significance of the novel insights and results derived‎. ‎In conclusion‎, ‎this research article offers a unique and innovative perspective on decision-making within the realm of the BDGF‎. ‎By employing the CPFFWA and the CPFFOWA operators‎, ‎organizations can make well-informed decisions to optimize their BDGF implementations‎, ‎mitigate uncertainties‎, ‎and harness the full potential of their data assets in an ever-evolving data landscape‎. ‎This work contributes to the advancement of decision support systems for big data governance (BDG)‎, ‎providing valuable insights for practitioners and scholars alike‎.

المصادر:

[1] Akram M, Bashir A. Complex fuzzy ordered weighted quadratic averaging operators. Granul Comput. 2021; 6: 523-538. DOI: https://doi.org/10.1007/s41066-020-00213-7
[2] Akram M, Bashir A, Garg H. Decision-making model under complex picture fuzzy Hamacher aggregation operators. Computational and Applied Mathematics. 2020; 39: 1-38. DOI: ‎http://doi.org/10.1007/s40314-020-01251-2
[3] Akram M, Dudek WA, Dar JM. Pythagorean dombi fuzzy aggregation operators with application in multi-criteria decision-making. International Journal of Intelligent Systems. 2019; 34(11): 3000-3019. DOI: https://doi.org/10.1002/int.22183
[4] Akram M, Dudek WA, Ilyas F. Group decision making based on Pythagorean fuzzy TOP-SIS method. International Journal of Intelligent Systems. 2019; 34(7): 1455-1475. DOI:
https://doi.org/10.1002/int.22103
[5] Akram M, Garg H, Zahid K. Extensions of ELECTRE-I and TOPSIS methods for group decision-making under complex Pythagorean fuzzy environment. Iranian Journal of Fuzzy Systems. 2020; 17(5): 147-164. DOI: ‎http://doi.org/10.22111/IJFS.2020.5522
[6] Akram M, Khan A. Complex Pythagorean Dombi fuzzy graphs for decision making. Granul Comput. 2021; 6: 645-669. DOI: https://doi.org/10.1007/s41066-020-00223-5
[7] Ali J, Naeem M, Alkenani AN. Complex T-Spherical Fuzzy Frank Aggregation Operators and Their Application to Decision Making. IEEE Access. 11: 88971-89023. DOI:
https://doi.org/10.1109/ACCESS.2023.3298845
[8] Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1986; 20(1): 8796. DOI: ‎http://doi.org/10.1007/978-3-7908-1870-3 1
[9] Beliakov G, Pradera A, Calvo T. Aggregation Functions: A Guide for Practitioners. Heidelberg: Springer; 2007. DOI: ‎http://doi.org/10.1007/978-3-540-73721-6
[10] Calvo T, Baets BD, Fodor J. The functional equations of Frank and Alsina for uni-norm and null-norms. Fuzzy Sets and System. 2001; 120(3): 385-394. DOI: https://doi.org/10.1016/S0165-0114(99)00125-6
[11] Casasnovas J, Torrens J. An axiomatic approach to fuzzy cardinalities of finite fuzzy sets. Fuzzy Sets and Systems. 2003; 133(2): 193-209. DOI: https://doi.org/10.1016/S0165-0114(02)00345-7
[12] Chen SM, Tan JM. Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems. 1994; 167(2): 163-172. DOI: https://doi.org/10.1016/0165-0114(94)90084-1
[13] Chiclana, F, Herrera, F, Herrera-Viedma, E. The ordered weighted geometric operator: Properties and application in MCDM problems. Technologies for Constructing Intelligent Systems 2: Tools. 2002; 173-183. DOI: ‎http://doi.org/10.1007/978-3-7908-1796-6 14
[14] Cuong, B. Picture fuzzy sets-first results. Part 1, in: seminar. Neuro-Fuzzy Systems with Applications. 2013.
[15] Cuong BC. Picture fuzzy sets first results, part 1, Seminar Neuro-Fuzzy Systems with Applications, [Preprint] 04/2013, Institute of Mathematics, Hanoi 2013. DOI: ‎http://doi.org/10.1109/WICT.2013.7113099
[16] Cuong BC. Picture fuzzy sets first results, part 2, Seminar Neuro-Fuzzy Systems with Applications, [Preprint] 04/2013, Institute of Mathematics, Hanoi, 2013.
[17] Cuong BC. Picture fuzzy sets. Journal of Computer Science and Cybernetics. 2014; 30(4): 409-420.
[18] Cuong, B. C, Kreinovich, V. (2013, December). Picture fuzzy sets-a new concept for computational intelligence problems. In 2013 third world congress on information and communication technologies (WICT 2013). 2013; p.1-6. DOI: ‎http://doi.org/10.1109/WICT.2013.7113099.
[19] Dinh NV, Thao NX. Some measures of picture fuzzy sets and their application in multi-attribute decision making. Int. J. Math. Sci. Comput. 2018; 4(3): 23-41. DOI: ‎http://doi.org/10.31130/jst.2017.49
[20] Fan CL, Song Y, Fu Q, Lei L, Wang X. New operators for aggregating intuitionistic fuzzy information with their application in decision making. IEEE Access. 2018; 6: 27214-27238. DOI: ‎http://doi.org/10.1109/AC-CESS.2018.2832206
[21] Morton A, Keisler J M, Salo A. Multicriteria portfolio decision analysis for project selection. Multiple criteria decision analysis: state of the art surveys. 2016; 1269-1298. DOI: ‎http://doi.org/10.1007/978-1-4939-3094-4 28
[22] Frank MJ. On the simultaneous associativity of F(x; y) and x+y -F(x; y). Aequationes Mathematicae. 1978; 18: 266-267. DOI: https://doi.org/10.1007/BF01844082
[23] Garg H. Some picture fuzzy aggregation operators and their applications to multicriteria decision making. Arabian Journal for Science and Engineering. 2017; 42(12): 5275-5290. DOI: ‎http://doi.org/10.1007/s13369-017-2625-9
[24] Garg H, Kaur G. Cubic intuitionistic fuzzy sets and its fundamental properties. Journal of Multiple-Valued Logic & Soft Computing. 2019; 33(6): 507-537.
[25] Garg H, Kumar K. Linguistic interval-valued atanassov intuitionistic fuzzy sets and their applications to group decision-making problems. IEEE Transactions on Fuzzy Systems. 2019; 27(12): 2302-2311. DOI: http://doi.org/10.1109/TFUZZ.2019.2897961
[26] Garg H, Rani D. Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process. ARABIAN JOURNAL for SCIENCE and ENGINEERING. 2019; 44: 2679-2698. DOI: http://doi.org/10.1007/s13369-018-3413-x
[27] Garg H, Rani D. Complex interval-valued intuitionistic fuzzy sets and their aggregation operators. Fundamenta Informaticae. 2019; 164(1): 61-101. DOI: ‎http://doi.org/10.3233/FI-2019-1755
[28] Hwang CL, Lai YJ, Liu TY. A new approach for multiple objective decision making. Computers & Operations Research. 1993; 20(8): 889-899. DOI: https://doi.org/10.1016/ 0305-0548(93)90109-V
[29] Iqbal W, Rehman AU, Farid G, Rathour L, Sharma MK, Mishra VN. Further on Petrovic's types inequalities. Journal of applied mathematics & informatics. 2022; 40(5-6): 1021-1034. DOI: https://doi.org/10.14317/jami.2022.1021
[30] Kaur G, Garg H. Generalized cubic intuitionistic fuzzy aggregation operators using t-norm operations and their applications to group decision-making process. Arabian Journal for Science and Engineering. 2019; 44: 2775-2794. DOI: ‎http://doi.org/10.1007/s13369-018-3532-4
[31] Khan S, Abdullah S, Ashraf S. Picture fuzzy aggregation information based on Einstein operations and their application in decision making. Mathematical Sciences. 2019; 13(3): 213-229. DOI: ‎http://doi.org/10.1007/s40096-019-0291-7
[32] Liao X, Li Y, Lu B. A model for selecting an ERP system based on linguistic information processing. Information Systems. 2007; 32(7): 1005-1017. DOI: https://doi.org/10.1016/j.is.2006.10.005
[33] Liu P, Akram M, Sattar A. Extensions of prioritized weighted aggregation operators for decision-making under complex q-rung ortho-pair fuzzy information. Journal of Intelligent & Fuzzy Systems. 2020; 39(5): 7469-7493. DOI: https://doi.org/10.3233/JIFS-200789
[34] Luqman A, Akram M, Al-Kenani AN, Alcantud JCR. A study on hypergraph representations of complex fuzzy information. Symmetry. 2019; 11(11): 1381. DOI: https://doi.org/10.3390/sym11111381
[35] Luqman A, Akram M, Smarandache F. Complex neutron sophic hypergraphs: new social network models. Algorithms. 2019; 12(11): 234. DOI: https://doi.org/10.3390/a12110234
[36] Mandal U, Seikh MR. Interval-valued spherical fuzzy MABAC method based on Dombi aggregation operators with unknown attribute weights to select plastic waste management process. Applied Soft Computing. 2023; 145: 110516. DOI: https://doi.org/10.1016/j.asoc.2023.110516
[37] Milosevic P, Dragovic I, Zukanovi M, Poledica A, Petrovic B. IFS-IBA Logical Aggregation with Frank t-norms. In: In Conference of the European Society for Fuzzy Logic and Technology. 2023. p.99-111. DOI: http://doi.org/10.1007/978-3-031-39965-7 9
[38] Mishra VN, Kumar T, Sharma MK, Rathour L. Pythagorean and fermatean fuzzy sub-group redefined in context of ~ T-norm and ~ S-conorm. Journal of Fuzzy Extension and Applications. 2023; 4(2): 125-135. DOI: https://doi.org/10.22105/jfea.2023.396751.1262
[39] Navara M. Triangular norms and conorms. Scholarpedia. 2007; 2(3): 2398. DOI: ‎http://doi.org/10.4249/scholarpedia.2398
[40] Pasi G, Yager RR. Modelling the concept of majority opinion in group decision making. Information Sciences. 2006; 176(4): 390-414. DOI: https://doi.org/10.1016/j.ins.2005.07.006
[41] Pitchipoo P, Vincent DS, Rajini N, Rajakarunakaran S. COPRAS decision model to optimize blind spot in heavy vehicles: A comparative perspective. Procedia Engineering. 2014; 97: 1049-1059. DOI: https://doi.org/10.1016/j.proeng.2014.12.383
[42] Qin J, Liu X. Frank aggregation operators for triangular interval type-2 fuzzy set and its application in multiple attribute group decision making. Journal of Applied Mathematics. 2014; 2014. DOI: https://doi.org/10.1155/2014/923213
[43] Qin J, Liu X, Pedrycz W. Frank aggregation operators and their application to hesitant fuzzy multiple attribute decision making. Applied Soft Computing. 2016; 41: 428-452. DOI:
https://doi.org/10.1016/j.asoc.2015.12.030
[44] Ramot D, Friedman M, Langholz G, Kandel A. Complex fuzzy logic. IEEE transactions on fuzzy systems. 2003; 11(4): 450-461. DOI: ‎http://doi.org/10.1109/TFUZZ.2003.814832
[45] Ramot D, Milo R, Friedman M, Kandel A. Complex fuzzy sets. IEEE transactions on fuzzy systems. 2002; 10(2): 171-186. DOI: ‎http://doi.org/10.1109/91.995119
[46] Rani D, Garg H. Distance measures between the complex intuitionistic fuzzy sets and its applications to the decision-making process. International Journal for Uncertainty Quantification. 2017; 7(5): 423-439. DOI: ‎http://doi.org/10.1615/Int.J.UncertaintyQuantification.2017020356
[47] Sarkoci P. Domination in the families of Frank and Hamacher t-norms. Kybernetika. 2005; 41(3): 349-360. DOI: ‎http://doi.org/10338.dmlcz/135660
[48] Sayadi MK, Heydari M, Shahanaghi K. Extension of VIKOR method for decision making problem with interval numbers. Applied Mathematical Modelling. 2009; 33(5): 2257-2262. DOI: https://doi.org/10.1016/j.apm.2008.06.002
[49] Seikh MR, Mandal U. Some picture fuzzy aggregation operators based on Frank t-norm and t-conorm: Application to MADM process. Informatica. 2021; 45(3): 447-461. DOI:
https://doi.org/10.31449/inf.v45i3.3025
[50] Seikh MR, Mandal U. Multiple attribute group decision making based on quasirung orthopair fuzzy sets: Application to electric vehicle charging station site selection problem. Engineering Applications of Artificial Intelligence. 2022; 115: 105299. DOI: https://doi.org/10.1016/j.engappai.2022.105299
[51] Seikh MR, Mandal U. Q-rung orthopair fuzzy Frank aggregation operators and its application in multiple attribute decision-making with unknown attribute weights. Granular Computing. 2022; 7: 709-730. DOI: http://doi.org/10.1007/s41066-021-00290-2
[52] Seikh MR, Mandal U. Interval-valued Fermatean fuzzy Dombi aggregation operators and SWARA based PROMETHEE II method to bio-medical waste management. Expert Systems with Applications. 2023; 226: 120082. DOI: https://doi.org/10.1016/j.eswa.2023.120082
[53] Shahzadi G, Akram M, Al-Kenani AN. Decision-making approach under Pythagorean fuzzy Yager weighted operators. Mathematics. 2020; 8(1): 70. DOI: https://doi.org/10.3390/math8010070
[54] Sharma MK, Chaudhary S, Rathour L, Mishra VN. Modified genetic algorithm with novel crossover and mutation operator in travelling salesman problem. Sigma Journal of Engineering and Natural Sciences. 2024; 42(6): XX-XX. DOI: http://doi.org/10.14744/sigma.2023.00105
[55] Sharma MK, Dhiman N, Kumar S, Rathour L, Mishra VN. Neutrosophic monte carlo simulation approach for decision making in medical diagnostic process under uncertain environment. Int J Neutrosophic Sci. 2023; 22(1): 08-16. DOI: https://doi.org/10.54216/IJNS.220101
[56] Sharma MK, Dhiman N, Mishra LN, Mishra VN, Sahani SK. Mediative fuzzy extension technique and its consistent measurement in the decision making of medical application. Mathematical Problems in Engineering. 2021; 2021: 1-9. DOI: https://doi.org/10.1155/2021/5530681
[57] Sharma MK, Sadhna A, Bhargava AK, Kumar S, Rathour L, Mishra LN, Pandey S. A fermatean fuzzy ranking function in optimization of intuitionistic fuzzy transportation problems. Advanced Mathematical Models & Applications. 2022; 7(2): 191-204.
[58] Shumaiza, Akram M, Al-Kenani AN, Alcantud JCR. Group decision-making based on the VIKOR method with trapezoidal bipolar fuzzy information. Symmetry. 2019; 11(10): 1313. DOI: https://doi.org/10.3390/sym11101313
[59] Ullah K, Mahmood T, Ali Z, Jan N. On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex & Intelligent Systems. 2020; 6: 15-27. DOI: ‎http://doi.org/10.1007/s40747-019-0103-6
[60] Ullah K, Naeem M, Hussain A, Waqas M, Haleemzai I. Evaluation of electric motor cars based Frank power aggregation operators under picture fuzzy information and a
multi-attribute group decision-making process. IEEE Access. 2023; 11: 67201-67219. DOI: http://doi.org/10.1109/ACCESS.2023.3285307
[61] Wang WS, He HC. Research on exible probability logic operator based on Frank T/S norms. Acta Electronica Sinica. 2009; 37(5): 1141-1145.
[62] Waseem N, Akram M, Alcantud JCR. Multi-attribute decision-making based on m-polar fuzzy Hamacher aggregation operators. Symmetry. 2019; 11(12): 1498. DOI: https://doi.org/10.3390/sym11121498
[63] Wei G. Picture fuzzy aggregation operators and their application to multiple attribute decision making. ournal of Intelligent & Fuzzy Systems. 2017; 33(2): 713-724. DOI: ‎http://doi.org/10.3233/JIFS-161798
[64] Wei G. Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Fundamental Informaticae. 2018; 157(3): 271-320. DOI: http://doi.org/10.3233/FI-2018-1628
[65] Wu SJ, Wei GW. Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. International Journal of Knowledge-Based and Intelligent Engineering Systems. 2017; 21(3): 189-201. DOI: https://doi.org/10.3233/KES-170363
[66] Xing Y, Zhang R,Wang J, Zhu X. Some new Pythagorean fuzzy Choquet-Frank aggregation operators for multi-attribute decision making. International Journal of Intelligent Systems. 2018; 33(11): 2189-2215. DOI: https://doi.org/10.1002/int.22025
[67] Xu Z. Intuitionistic fuzzy aggregation operators. IEEE Transactions on fuzzy systems. 2007; 15(6): 1179-1187. DOI: https://doi.org/10.1109/TFUZZ.2006.890678
[68] Xu Z, Yager RR. Some geometric aggregation operators based on intuitionistic fuzzy sets. International journal of general systems. 2006; 35(4): 417-433. DOI: https://doi.org/10.1080/03081070600574353
[69] Yager RR. On ordered-weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on systems, Man, and Cybernetics. 1988; 18(1): 183-190. DOI: ‎http://doi.org/10.1109/21.87068
[70] Yager RR. On some new classes of implication operators and their role in approximate reasoning. Information Sciences. 2004; 167(1-4): 193-216. DOI: https://doi.org/10.1016/j.ins.2003.04.001
[71] Yager RR. Pythagorean membership grades in multicriteria decision making. IEEE Transactions on fuzzy systems. 2013; 22(4): 958-965. DOI: ‎http://doi.org/10.1109/TFUZZ.2013.2278989
[72] Yang X, Mahmood T, Ali Z, Hayat K. Identification and classification of multi-attribute decision-making based on complex intuitionistic fuzzy Frank aggregation operators. Mathematics. 2023; 11(15): 3292. DOI: http://doi.org/10.3390/math11153292
[73] Yu PL. A class of solutions for group decision problems. Management science. 1973; 19(8): 936-946. DOI: https://doi.org/10.1287/mnsc.19.8.936
[74] Zadeh LA. Fuzzy sets. Information and Control. 1965; 8(3): 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
[75] Zavadskas EK, Kaklauskas A, Turskis Z, Tamosaitiene J. Selection of the effective dwelling house walls by applying attributes values determined at intervals. Journal of civil engineering and management. 2008; 14(2): 85-93. DOI: ‎http://doi.org/10.3846/1392-3730.2008.14.3
[76] Zhang G, Dillon TS, Cai KY, Ma J, Lu J. Operation properties and $\delta$-equalities of complex fuzzy sets. International Journal of Approximate Reasoning. 2009; 50(8): 1227-1249. DOI: https://doi.org/10.1016/j.ijar.2009.05.010
[77] Zhou LP, Dong JY, Wan SP. Two new approaches for multi-attribute group decision making with interval-valued neutron-sophic Frank aggregation operators and incomplete weights. IEEE Access. 2019; 7: 102727-102750. DOI: ‎http://doi.org/10.1109/ACCESS.2019.2927133